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Do Bees Build It Best? GeometryTrigonometry

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BUILDING THE BEST

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NAILING DOWN AREA

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HOW MANY CAN YOU FIND?

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THATS ALL THERE IS!

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HALVING YOUR WAY

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PARALLELOGRAMS AND TRAPEZOIDS

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FORMING FORMULAS

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GOING INTO THE GALLERY

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A RIGHT-TRIANGLE PAINTING

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A TRIGONOMETRIC SUMMARY

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MORE GALLERY MEASUREMENTS

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A HOMEMADE TRIG TABLE

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SHADOWS AND SAILBOATS

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TRI-SQUARE RUG GAMES

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ANY TWO SIDES WORK n LEG^2 + LEG^2 = HYP^2

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IMPOSSIBLE RUGS

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MAKE THE LINES COUNT

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PROOF BY RUGS

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THE POWER OF PYTHAGORAS

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LESLIES FERTILE FLOWERS

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FLOWERS FROM DIFFERENT SIDES

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DONT FENCE ME IN

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RECTANGLES ARE BORING!

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MORE FENCING, BIGGER CORRALS

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MORE OPINIONS ABOUT CORRALS

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BUILDING THE BEST FENCE

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FALLING BRIDGES

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LESLIES FLORAL ANGLES

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FLAT CUBES

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FLAT BOXES

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A VOLUMINOUS TASK

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PUT YOUR FIST INTO IT

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THE INS AND OUTS OF BOXES

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A SCULPTURE GARDEN

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THE WORLD OF PRISMS

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SHEDDING LIGHT ON PRISMS

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PYTHAGORAS AND THE BOX

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BACK ON THE FARM

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WHICH HOLDS MORE?

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CEREAL BOX SIZES

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A-TESSELLATING WE GO

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A PORTFOLIO OF FORMULAS

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THATS ALL THERE IS! n EACH TRIANGLE MUST HAVE AN AREA OF 2 UNITS n EACH TRIANGLE MUST HAVE ITS VERTICES ON PEGS n EACH TRIANGLE MUST HAVE A HORIZONTAL SIDE

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HALVING YOUR WAY

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FORMING FORMULAS n LOOK FOR WAYS TO CUT UP THE PARALLELOGRAMS AND TRAPEZOIDS INTO TRIANGLES

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GOING INTO THE GALLERY n REMEMBER, THE HEIGHT IS ALSO THE ALTITUDE WHICH IS DRAWN PERPENDICULAR TO THE BASE

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A RIGHT-TRIANGLE PAINTING n DRAW A RIGHT TRIANGLE THAT HAS A 55 DEGREE ANGLE n EXTEND BOTH SIDES SO THAT THEY ARE AT LEAST 10 CM IN LENGTH

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A TRIGONOMETRIC SUMMARY n SIN A = OPPOSITE/HYPOTENUSE n COS A = ADJACENT/HYPOTENUSE n TAN A = OPPOSITE/ADJACENT

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A HOMEMADE TRIG TABLE n DRAW A RIGHT TRIANGLE USING THE ASSIGNED ANGLE FOR YOUR GROUP n MEASURE ALL THE SIDES n COMPUTE THE RATIOS OF SIN, COS, AND TAN

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MORE GALLERY MESUREMENTS n SIN A = OPPOSITE/HYPOTENUSE n COS A = ADJACENT/HYPOTENUSE n TAN A = OPPOSITE/ADJACENT

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SHADOWS AND SAILBOATS

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TRI-SQUARE RUG GAMES n AL WINS WHEN THE LARGEST OF THE 3 SQUARES HAS THE MOST AREA. n WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

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TRI-SQUARE RUG GAMES n BETTY WINS IF THE TWO SMALLER SQUARES HAVE MORE AREA THEN THE LARGEST n WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

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TRI-SQUARE RUG GAMES n IF THE TWO SMALLER SQUARES HAVE THE SAME AREA AS THE LARGEST, THIS IS A FAIR GAME. n WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

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ANY TWO SIDES WORK

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IMPOSSIBLE RUGS n RULE: ANY TWO SIDES OF A TRIANGLE MUST BE GREATER THAN THE THIRD SIDE

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MAKE THE LINES COUNT

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THE POWER OF PYTHAGORAS

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LESLIES FERTILE FLOWERS

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FLOWERS FROM DIFFERENT SIDES

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DONT FENCE ME IN n n RANCHER GONZALES CAN ONLY AFFORD 300 FEET OF FECNING n n MAKE AN INOUT TABLE OF VARIOUS LENGTHS AND WIDTHS

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RECTANGLES ARE BORING! n RANCHER GONZALES NEPHEW JUAN HAS SUGGESTED RECTANGLES n AGAIN SHE MUST USE 300 FEET OF FENCING

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MORE FENCING, BIGGER CORRALS n HOW DOES THE AREA OF A SQUARE CORRAL MADE 300 FT OF FENCING COMPARE TO 600 FT?

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MORE FENCING, BIGGER CORRALS n HOW DOES THE AREA OF A AN EQUILATERAL TRIANGLE CORRAL MADE 300 FT OF FENCING COMPARE TO 600 FT?

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MORE OPINIONS ABOUT CORRALS n ACES : PENTAGON n TWOS: HEXAGON n THREES: SEPTAGON n FOURS: OCTAGON n FIVES: 9 SIDED REG-POLY n SIXES: 10 SIDED REG-POLY

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BUILDING THE BEST FENCE n AREA= (P^2/4n) * tan (90-180/n)

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FALLING BRIDGES n USE OTHER APPROXIMATIONS FOR THE SQUARE ROOT OF 2

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LESLIES FLORAL ANGLES n REMEMBER, THE INVERSE OF: ADDING?MULTIPLYING? SOMETHING SQUARED? n NOW WE NEED THE INVERSE OF OUR TRIG FUNCTIONS

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FLAT BOXES n 132 CM SQUARED

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FLAT BOXES n 108 CM SQUARED

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A VOLUMINOUS TASK SURFACE AREAVOLUME n #1 n #2 n #3 n #4 n #5

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A VOLUMINOUS TASK SURFACE AREAVOLUME n #7 n #8 n #9 n #10

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PUT YOUR FIST INTO IT

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THE INS AND OUTS OF BOXES

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A SCULPTURE GARDEN n FIND A WAY TO ARRANGE 8 CUBES THAT USES THE LEAST AMOUNT OF PAINT

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THE WORLD OF PRISMS n PRISM IS A SPECIAL TYPE OF SOLID GEOMETRIC FIGURE –THE INTIAL AND FINAL FACES ARE THE BASES –USUALLY 1 OR 2 BASES –PERPENDICULAR DISTANCE BETWEEN THE BASES IS THE HEIGHT

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THE WORLD OF PRISMS n TRIANGULAR PRISMS n HEXAGONAL PRISMS n RECTANGULAR PRISMS

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THE WORLD OF PRISMS n RIGHT PRISMS n OBLIQUE PRISMS

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THE WORLD OF PRISMS n LATERAL FACES n LATERAL EDGES n BASES n LATERAL SURFACE AREA n TOTAL SURFACE AREA

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PYTHAGORAS AND THE BOX

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BACK ON THE FARM

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